Sc@B28−, Ti@B28, V@B28+, and V@B292−: Spherically Aromatic Endohedral Seashell-like Metallo-Borospherenes

Transition-metal-doped boron nanoclusters exhibit unique structures and bonding in chemistry. Using the experimentally observed seashell-like borospherenes C2 B28−/0 and Cs B29− as ligands and based on extensive first-principles theory calculations, we predict herein a series of novel transition-metal-centered endohedral seashell-like metallo-borospherenes C2 Sc@B28− (1), C2 Ti@B28 (2), C2 V@B28+ (3), and Cs V@B292− (4) which, as the global minima of the complex systems, turn out to be the boron analogues of dibenzenechromium D6h Cr(C6H6)2 with two B12 ligands on the top and bottom interconnected by four or five corner boron atoms on the waist and one transition-metal “pearl” sandwiched at the center in between. Detailed molecular orbital, adaptive natural density partitioning (AdNDP), and iso−chemical shielding surface (ICSS) analyses indicate that, similar to Cr(C6H6)2, these endohedral seashell-like complexes follow the 18-electron rule in bonding patterns (1S21P61D10), rendering spherical aromaticity and extra stability to the systems.


Structures and Stabilities
The obtained transition-metal-centered seashell-like metallo-borospherenes C 2 Sc@B 28 − (1), C 2 Ti@B 28 (2), C 2 V@B 28 + (3), and C s V@B 29 2− (4) as the GMs of the systems at PBE0/6-311+G(d) [51], TPSSh/6-311+G(d) [52,53], and CCSD(T)/6-31G(d) [54,55] levels are collectively depicted in Figure 1, with more alternative low-lying isomers summarized in Figures S1-S4 (ESI †). The isovalent Sc@B 28 − (1), Ti@B 28 (2), and V@B 28 + (3) with the calculated coordination energies of E c = 9.56, 7.83, 7.57 eV and lowest calculated vibration frequencies of 181.13, 186.63, 184.70 cm −1 at PBE0, respectively, turn out to have similar seashell-like structures in the same symmetry as their parent C 2 B 28 ligand [7], with two B 12 ligands on the top and bottom interconnected by four corner boron atoms on the waist and one transition metal pearl comfortably sandwiched in between. These axially chiral endohedral metallo-borospherene complexes contain a slightly distorted C 2 B 16 double-ring tube as the basis of the seashell-like structures, two heptagonal windows on the right and left, and thirty-six B 3 triangles on the cage surface, with a transition metal center sandwiched comfortably inside the B 28 cage along the C 2 molecular axis on the upper end of the B 16 double-ring tube (see detailed coordination bond lengths tabulated in Table S1). (1), Ti@B 28 (2), V@B 28 + (3) possess the large calculated HOMO-LUMO energy gaps of ∆E gap = 2.10, 2.97, and 3.20 eV at PBE0, respectively, well supporting their high chemical stabilities. It is noticed that the second isomer C 2 Sc&B 28 − (1b) in Figure S1, an exohedral metallo-borospherene with an octacoordinate Sc atom at the lower end of the B 16 doublering tube, is actually iso-energetic with Sc@B 28 − (1) at CCSD(T), suggesting that the two degenerate C 2 isomers may coexist in experiments, while, as shown in Figures S2 and S3, the endohedral Ti@B 28 (2) and V@B 28 + (3) are 0.18 eV and 0.04 eV more stable than their second lowest-lying isomers at CCSD(T), respectively. Triplet and quintet isomers prove to be at least 0.85 eV less stable than their singlet GMs.
Molecules 2023, 28, x FOR PEER REVIEW 3 of 10 the basis of the seashell-like structures, two heptagonal windows on the right and left, and thirty-six B3 triangles on the cage surface, with a transition metal center sandwiched comfortably inside the B28 cage along the C2 molecular axis on the upper end of the B16 doublering tube (see detailed coordination bond lengths tabulated in Table S1). C2 Sc@B28 − (1), Ti@B28 (2), V@B28 + (3) possess the large calculated HOMO-LUMO energy gaps of ΔEgap = 2.10, 2.97, and 3.20 eV at PBE0, respectively, well supporting their high chemical stabilities. It is noticed that the second isomer C2 Sc&B28 − (1b) in Figure S1, an exohedral metalloborospherene with an octacoordinate Sc atom at the lower end of the B16 double-ring tube, is actually iso-energetic with Sc@B28 − (1) at CCSD(T), suggesting that the two degenerate C2 isomers may coexist in experiments, while, as shown in Figure S2 and Figure S3, the endohedral Ti@B28 (2) and V@B28 + (3) are 0.18 eV and 0.04 eV more stable than their second lowest-lying isomers at CCSD(T), respectively. Triplet and quintet isomers prove to be at least 0.85 eV less stable than their singlet GMs. The optimized V-centered Cs V@B29 2− (4) also possesses a seashell-like endohedral structure in the same symmetry as its parent ligand Cs B29 − [8]. It contains two B12 ligands on the top and bottom interconnected by five corner boron atoms on the waist, two equivalent octagonal windows on the right and left sides, and thirty-eight B3 triangles on the cage surface, with a vanadium center coordinated inside. With a large calculated HOMO-LUOM energy gap of ΔEgap = 2.39 eV, coordination energy of Ec = 4.79 eV and one small imagery vibrational frequency at -54.30 cm -1 , Cs V@B29 2− (4) appears to be the vibrationally averaged GM of the system between two slightly distorted C1 V@B29 2− isomers (4b in Figure S4) in an a″ vibrational mode in which the top B atom and V center swinging left and right reversibly. With zero-point corrections included, Cs V@B29 2− (4) turns out to be 0.02 eV and 0.06 eV more stable than the second seashell-like isomer C1 V@B29 2− (4b) and third tubular isomer Cs V@B29 2− (4c) at CCSD(T), respectively ( Figure S4). Triplet and quintet isomers are found to be 0.74 eV and 1.81 eV less stable than singlet Cs V@B29 2− (4) at PBE0 level, respectively, and all the other isomers lying at least 0.15 eV higher than the Cs GM (4).
Detailed natural bonding orbital (NBO) [56] analyses indicate that transition metal centers in Sc@B28 − (1), Ti@B28 (2) , and total Wiberger bond orders of 4.03, 6.02, 6.70, and 6.44, respectively. Obviously, transition metal coordination centers in these complexes donate their 4s 2 electrons almost completely to the boron ligands, while in return, accept partial electrons in their partially filled 4d orbitals from the boron ligands via effective π→3d back-donations, enhancing the thermodynamical stabilities of systems.
Extensive Born-Oppenheimer molecular dynamics (BOMD) [57] simulations on Sc@B28 − (1) at 600 K, Ti@B28 (2) at 700 K, and V@B29 2− (4) at 700 K in Figure S5 clearly indicate that these seashell-like transition metal boron complexes are highly dynamically stable at high temperatures, as evidenced by their small calculated root-mean-square-deviations of RMSD = 0.09, 0.10, 0.10 Å and maximum bond length deviations of MAXD = 0.30, 0.32, 0.33 Å, respectively. No high-lying isomers were observed during the simulations in 30 The optimized V-centered C s V@B 29 2− (4) also possesses a seashell-like endohedral structure in the same symmetry as its parent ligand C s B 29 − [8]. It contains two B 12 ligands on the top and bottom interconnected by five corner boron atoms on the waist, two equivalent octagonal windows on the right and left sides, and thirty-eight B 3 triangles on the cage surface, with a vanadium center coordinated inside. With a large calculated HOMO-LUOM energy gap of ∆E gap = 2.39 eV, coordination energy of E c = 4.79 eV and one small imagery vibrational frequency at −54.30 cm −1 , C s V@B 29 2− (4) appears to be the vibrationally averaged GM of the system between two slightly distorted C 1 V@B 29 2− isomers (4b in Figure S4) in an a" vibrational mode in which the top B atom and V center swinging left and right reversibly. With zero-point corrections included, C s V@B 29 2− (4) turns out to be 0.02 eV and 0.06 eV more stable than the second seashell-like isomer C 1 V@B 29 2− (4b) and third tubular isomer C s V@B 29 2− (4c) at CCSD(T), respectively ( Figure S4). Triplet and quintet isomers are found to be 0.74 eV and 1.81 eV less stable than singlet C s V@B 29 2− (4) at PBE0 level, respectively, and all the other isomers lying at least 0.15 eV higher than the C s GM (4).
Detailed natural bonding orbital (NBO) [56] analyses indicate that transition metal centers in Sc@B 28 − (1), Ti@B 28 (2) (1) at 600 K, Ti@B 28 (2) at 700 K, and V@B 29 2− (4) at 700 K in Figure S5 clearly indicate that these seashell-like transition metal boron complexes are highly dynamically stable at high temperatures, as evidenced by their small calculated root-mean-square-deviations of RMSD = 0.09, 0.10, 0.10 Å and maximum bond length deviations of MAXD = 0.30, 0.32, 0.33 Å, respectively. No high-lying isomers were observed during the simulations in 30 ps, with the basic structural motifs of the complex systems well maintained in reversible thermal vibrations.
ps, with the basic structural motifs of the complex systems well maintained in reversible thermal vibrations.
Cs V@B29 2-(4) appears to possess a similar bonding pattern. As shown in Figure 2c, it has 38 3c-2e σ bonds on 38 B3 triangles on the cage surface, forming the σ-framework of the B29 -ligand. The remaining nine delocalized coordination bonds include three 13c-2e B12 (π)-V(dπ/σ) bonds between the V center and B12 ligand on the top, three 13c-2e B12 (π)-V (dπ/σ) between the V center and B12 ligand at the bottom, and three 27c-2e B14 (π)-V Detailed AdNDP analyses presented in Figure 2b indicate that neutral seashell-like C 2 Ti@B 28 (2) contains 34 3c-2e σ bonds on 34 B 3 triangles on the cage surface and 1 4c-2e σ bond shared by two edge-sharing B 3 triangles on the upper end, forming the σ-framework of the seashell-like complex. Its remaining nine delocalized coordination bonds include three 13c-2e B 12 (π)-Ti (d π/σ ) bonds between the Ti center and B 12 ligand on the top, three 13c-2e B 12 (π)-Ti (d π/σ ) between the Ti center and B 12 ligand at the bottom, and three 27c-2e B 13 (π)-Ti (d π/σ )-B 13 (π) bonds mainly between Ti and its two B 12 ligands on the top and bottom with ON = 1.88~2.00 |e|. Such a delocalized coordination bonding pattern possesses a one-to-one correspondence relationship with that of D 6h (C 6 H 6 ) 2 Cr in Figure 2a, indicating that, similar to (C 6 H 6 ) 2 Cr, Ti@B 28 (2) follows the 18-electron principle in coordination bonding pattern. Both the isovalent C 2 Sc@B 28 − (1) and C 2 V@B 28 + (3) are found to follow similar bonding patterns ( Figure S6). C s V@B 29 2− (4) appears to possess a similar bonding pattern. As shown in Figure 2c, it has 38 3c-2e σ bonds on 38 B 3 triangles on the cage surface, forming the σ-framework of the B 29 − ligand. The remaining nine delocalized coordination bonds include three 13c-2e B 12 (π)-V(d π/σ ) bonds between the V center and B 12 ligand on the top, three 13c-2e B 12 (π)-V (d π/σ ) between the V center and B 12 ligand at the bottom, and three 27c-2e B 14 (π)-V (d π/σ )-B 12 (π) bonds mainly between V and its two B 12 ligands on the top and bottom with ON = 1.91~1.99 |e|, again well corresponding to bonding pattern of D 6h (C 6 H 6 ) 2 Cr in Figure 2a, showing that V@B 29 2− (4) also matches the 18-electron rule in coordination bonding pattern.
The calculated iso-chemical shielding surfaces (ICSSs) [61] of Ti@B 28 (2) and V@B 29 2− (4) based on the ZZ components of the calculated nuclear-independent chemical shifts (NICS-ZZ) shown in Figure 3a,c appear to be similar with that of the experimentally known spherically aromatic C 2 B 28 (Figure 3b) [7] and C s B 29 − (Figure 3d) [8], respectively, well supporting the spherical aromaticity of these endohedral seashell-like endohedral complexes. The spaces inside the boron cage or within 1 Å above the cage surface in vertical directions with negative NICS-ZZ values belong to chemical shielding regions (highlighted in yellow), while the belt-like region outside the cage in the horizontal direction around the waist belongs to the chemical de-shielding area (highlighted in green).
The calculated iso-chemical shielding surfaces (ICSSs) [61] of Ti@B28 (2) and V@B29 2-(4) based on the ZZ components of the calculated nuclear-independent chemical shifts (NICS-ZZ) shown in Figure 3a,c appear to be similar with that of the experimentally known spherically aromatic C2 B28 (Figure 3b) [7] and Cs B29 - (Figure 3d) [8], respectively, well supporting the spherical aromaticity of these endohedral seashell-like endohedral complexes. The spaces inside the boron cage or within 1 Å above the cage surface in vertical directions with negative NICS-ZZ values belong to chemical shielding regions (highlighted in yellow), while the belt-like region outside the cage in the horizontal direction around the waist belongs to the chemical de-shielding area (highlighted in green).

IR, Raman, and PE Spectral Simulations
Joint experimental spectroscopic and first-principles theory investigations have proven to be the most effective method to characterize gas phase clusters [62]. The infrared (IR) and Raman spectra of C2 Sc@B28 -(1), C2 Ti@B28 (2), and Cs V@B29 2-(3) are simulated at PBE0/6-311+G(d) in Figure 4 to facilitate their future spectroscopic characterizations. As shown in Figure 4a

IR, Raman, and PE Spectral Simulations
Joint experimental spectroscopic and first-principles theory investigations have proven to be the most effective method to characterize gas phase clusters [62]. The infrared (IR) and Raman spectra of C 2 Sc@B 28 − (1), C 2 Ti@B 28 (2), and C s V@B 29 2− (3) are simulated at PBE0/6-311+G(d) in Figure 4 to facilitate their future spectroscopic characterizations. As shown in Figure 4a Figure 4c). Simulated IR and Raman spectra of (a) C 2 V@B 28 + are shown in Figure S8.

Computational Details
Extensive GM searches were performed on Sc@B 28 − , Ti@B 28 , and V@B 28 + , V@B 29 2− at DFT level with electronic multiplicities considered, using both the TGmin2 [66,67] and Minima Hopping (MH) [68,69] codes, in conjunction with manual constructions based on the experimentally observed C 2 B 28 −/0 and C s B 29 − at PBE/DZVP, with about 3500 stationary points probed for each species on its potential surface. The low-lying isomers were then fully optimized at both PBE0/6-311+G(d) [51] and TPSSh/6-311+G(d) [52,53] levels using the Gaussian 09 program, with vibrational frequencies checked to make sure all the obtained low-lying isomers are true minima of the systems. Single point CCSD(T)/6-31G(d) calculations were performed on the five lowest-lying isomers to further refine their relative energies employing the Molpro (2013) program [54,55], with the T 1 diagnostics checked to make sure that multi-reference interactions make non-significant contributions in these closed-shell complexes. Natural bonding orbital (NBO) analyses were carried out using the NBO 6.0 program [56]. Extensive Born-Oppenheimer molecular dynamics (BOMD) simulations were performed on C 2 Sc@B 28 − (1) at 600 K, C 2 Ti@B 28 (2) at 700 K, and V@B 29 2− (4) at 700 K for 30 ps using the CP2K program [57] utilizing the hybrid Gaussian and plane waves method, with the GTH-PBE pseudopotential and DZVP-MOLOPT-SR-GTH basis set for boron and transition metal, respectively. Detailed bonding analyses were carried out utilizing the adaptive natural density partitioning (AdNDP) approach [58,59]. Iso-chemical shielding surfaces (ICSS) [61] were calculated using the Multiwfn 3.8 software [70]. Bonding analyses and ICSS surfaces were visualized using the visual molecular dynamics (VMD) [71] software. The IR and Raman spectra of C 2 Sc@B 28 − (1), C 2 Ti@B 28 (2), C s V@B 29 2− (4) were simulated at PBE0/6-311+G(d). The PE spectra of C 2 Sc@B 28 − (1), C 1 Ti@B 28 − and C s V@B 29 − were simulated using the time-dependent DFT approach (TD-DFT) at PBE0/6-311+G(d) level [64,65]. An overall calculation scheme used in this work is presented in Figure S9.

Conclusions
Based on the experimentally observed seashell-like C 2 B 28 −/0 and C s B 29 − and extensive first-principles theory calculations, we propose in this work the transition-metalcentered endohedral seashell-like metallo-borospherenes Sc@B 28 − (1), Ti@B 28 (2), V@B 28 + (3), and V@B 29 2− (4) which, as the boron analogues to the well-known sandwich complex Cr(C 2 H 6 ) 2 highly stable both thermodynamically and dynamically, follow the 18-electron rule in coordination bonding patterns and are spherically aromatic in nature. The IR, Raman, and PE spectra of the concerned species are theoretically simulated to facilitate their future spectroscopic characterizations in gas-phase experiments via laser ablations of boron-transition-metal mixed binary targets. Further combined theoretical and experimental investigations on metal-doped boron complexes are expected to unveil novel structures and bonding in chemistry and materials science and shed new insights on boron-based nano-devices.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/molecules28093892/s1, Figure S1: Low-lying isomers of C 2 Sc@B 28 − with their relative energies; Figure S2: Low-lying isomers of C 2 Ti@B 28 with their relative energies; Figure S3: Low-lying isomers of C 2 V@B 28 + with their relative energies; Figure S4: Low-lying isomers of C s V@B 29 2− with their relative energies; Figure S5: Molecular dynamics simulations of (a) Sc@B 28

−
(1) at 600 K, (b) Ti@B 28 (2) at 700 K, and (c) V@B 29 2− (4) at 700 K; Figure S6: AdNDP Analysis of (a) C 2 Sc@B 28 − and (b) C 2 V@B 28 + ; Figure S7: Molecular orbital energy levels of (a) D 6h (C 6 H 6 ) 2 Cr, (b) C 2 Ti@B 28 and (c) C s V@B 29 2− ; Figure S8: Simulated IR and Raman spectra of (a) C 2 V@B 28 + ; Figure S9: An overall scheme of the theoretical procedures adapted in this work. Table S1: The bond lengths r Sc-B of C 2 Sc@B 28 − , r Ti-B of C 2 Ti@B 28 , r V-B of C 2 V@B 28 and r' V-B of C s V@B 29 2− ; Table S2: Cartesian coordinates of the optimized low-lying isomers.  Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.

Conflicts of Interest:
The authors declare no conflict of interest.
Sample Availability: Samples of the compounds are not available from the authors.